Decompositions of stochastic convolution driven by a white-fractional Gaussian noise

Let u = {u(t, x); (t, x) is an element of DOUBLE-STRUCK CAPITAL R+ x is an element of} be the solution to a linear stochastic heat equation driven by a Gaussian noise, which is a Brownian motion in time and a fractional Brownian motion in space with Hurst parameter H is an element of (0, 1). For any given x is an element of DOUBLE-STRUCK CAPITAL R (resp., t is an element of DOUBLE-STRUCK CAPITAL R+), we show a decomposition of the stochastic process t -> u(t, x) (resp., x -> u(t, x)) as the sum of a fractional Brownian motion with Hurst parameter H/2 (resp., H) and a stochastic process with C-infinity-continuous trajectories. Some applications of those decompositions are discussed.